Why? Encrypting e-mail addresses would break password reset features and phone numbers are generally public anyway (yes you can go X-directory, but the real issue here is why these services require a valid phone number to begin with)
It's also worth noting that it wouldn't just be the web servers that require your private key, it would also be any mail servers you use for sending your newsletters and such like (assuming these aren't run on your web servers - which often isn't the case). Then there's your telephone support staff, who would also may need to know your e-mail address so they could do their job effectively. And any other operators that might compile data extracts, eg for 3rd parties where users have given permission for your details to used / sold.
Quickly you're in a situation where your private key is more available across your infrastructure than the e-mail would have been if it wasn't encrypted to begin with.
Now lets look at the cost of such a system. There's an obvious electricity / hardware cost with the CPU time required to encrypt / decrypt this data (after all, CPU time is the general measure for the strength of encryption) and the staffing cost with the time wasted jumping through those extra hoops. The development time, code complexity, etc - it all has a cost to the company.
So what's the benefits in any companies doing this? They don't gain any extra security? This is really more of a privacy policy for their users; and users which are that paranoid about their e-mail address being leaked should either use a disposable e-mail account or shouldn't be using a cloud-based proprietary messenging network to begin with. What's more the chat history might well have your e-mail address in anyway (eg "hi dave, I'm heading into a meeting shortly, but e-mail me at bob@example.com and I'll have a look tonight")
Don't get me wrong, I'm all for hashing / encrypting sensitive data. But pragmatically we need to consider:
1) are e-mail addresses really that sensitive? Or instead should we be encouraging better security for our web-mail et al accounts (eg 2 factor authentication) to prevent our addresses being abused. Given that we give out e-mail addresses to anyone who needs to contact us, I think the latter option (securing our email accounts) is the smarter one
2) instead of encrypting phone numbers and postal addresses, should we instead be challenging the requirement for online services to store them to begin with? If they have my email address, why do they also need my phone number? Postal address I can forgive a little more if there's a product that needs shipping or payments that need to be made.